CASM Winter Masterclass in Mathematical and Computational Finance for Scientists and Engineers

Date: 26 – 30 December 2018

The pace at which modern finance continues to grow has been possible due to the availability of advanced mathematics and computational power. At the centre of these advances is the noticeable contribution of graduates trained in hard science, computing and engineering disciplines. This has allowed the financial markets to become increasingly sophisticated as well as the emergence of new complex financial products and markets. Alternative names for this branch of mathematical science are Mathematical Finance, Financial Mathematics and Financial Engineering. All of them rely on the provision of well-trained scientists with interests in finance.

In recent years, there has been an explosion in the availability and popularity of advanced degrees in Mathematical Finance and Computational Finance at many of the top tier universities internationally. These are aimed at leading numerate graduates towards lucrative and technically challenging careers as quantitative analysts (quants), developers and traders in investment banks and hedge funds. They are typically taught MSc degrees of ten-months duration, with increasing numbers of graduates from Pakistan being attracted to Europe, USA and Australasia for advanced scholarship in this field.


The programme comprising of lectures and lab sessions will be delivered over five days. The proposed audience for this intensive workshop are junior/senior majors following degrees in maths, computer science, physics or engineering, as well as graduate students. In addition, the workshop is open to industry professionals working in banks, actuarial firms, financial technology, securities and exchange, financial regulation.

The aim of the course is to present a combination of the mathematical and computational based concepts which have practical uses in the global financial sector. However, the interdisciplinary nature of the material makes these topics transferable to other industry groups. Take-home exercises will be available.

Participants for the workshop should have studied basic probability and partial differential equations as part of their undergraduate training. Introduction to programming in Python will be given. No previous knowledge of finance is required. A certificate of participation will be awarded to all participants.

Course Outline

Day 1

Finance Terminology: Finance terms used in the markets. Compounding, discounting. Asset classes. Futures/Forwards. Options, payoff and P&L.

Binomial Model: No arbitrage, delta hedging. Replicating strategy. Risk-neutral probabilities.

Day 2

Applied Stochastic Calculus: Construction of Brownian motion and properties. Stochastic Differential Equations – drift, diffusion. Itô’s lemma. Asset price models for stocks – Geometric Brownian Motion. Transition densities, Forward and Backward Kolmogorov equations.

Risk & Reward: Portfolio Optimisation – benefits of diversifying

Day 3

Black-Scholes framework: Classic Black-Scholes assumptions, PDE and Nobel prize winning solution. Simple European calls and puts. Discontinuous payoffs – Binary and Digital options.

Volatility Modelling: Importance and different types of volatility Actual, realised, implied and stochastic. Local volatility and volatility surfaces. Popular stochastic volatility models.

Exotics: Path dependent options – Asians and Lookbacks

Day 4

Computational Finance: Monte Carlo methods for evaluating integrals and link to expectations. Derivative pricing.

Python Lab Session: Pricing options using the Monte Carlo Method.

Day 5

Fixed-Income World: Fixed-Income products and markets. One factor stochastic interest-rate models. Bond Pricing Equation (BPE). Tractable models and Affine Solutions. Popular spot rate models. Calibration. HJM and modelling the whole yield curve. Market Models and BJM.

Nonlinear Black-Scholes Modelling: The uncertain parameter framework – volatility, interest rates and dividends.

The workshop will be delivered by mathematicians who all have interests and skills in technical finance; at both academic and practitioner levels.

Dr Sultan Sial (LUMS faculty and Programme Director)

Sultan received the MSc. Mathematics degree from Carleton University and the PhD. degree in Applied Mathematics from University of Western Ontario, Canada in 1992 and 1997, in turn. Prior to LUMS, he has been associated with Universities of Toronto and Western Ontario; Los Alamos National Lab; and Trent University. Sultan has corporate sector experience; he has been the Vice President (Research) of Heuchera Technologies, and Vogelfrei Analytics. He has several publications, a book and book chapter in leading international journals.

Dr Adnan Khan (LUMS Faculty)

Adnan’s Ph.D. titled ‘Parameterization for Some Multiscale Problems in Biology and Turbulence’ was awarded in 2007 by Rensselaer Polytechnic Institute (RPI) in NY. The research involved approaches to coarse graining of multiscale systems with applications to turbulent diffusion and protein dynamics. In 2002 he completed a MS in Applied Mathematics from the University of Delaware. Current research interests include modelling and examination of biological systems, multiscale modelling and asymptotic analysis. Prior to LUMS, he taught at RPI and University of Delaware. Besides the usual academic interests, he is also interested in reading on economics, philosophy, history and world literature.

Dr Riaz Ahmad (Overseas Visiting Faculty)

Riaz is visiting LUMS as part of the global engagement project funded by University College London (UCL). He has over fifteen years of industry experience in the financial services sector; and has been visiting LUMS for 20 years.

Dr Azmat Hussain (LUMS Faculty)

Azmat obtained his PhD in Operations Research from North Carolina State University in 2016, while he was the recipient of a Fulbright Scholarship. His PhD research focused on optimization problems for stochastic systems with memory. Earlier research work has centred on fluid dynamics. Prior to LUMS Azmat lectured at Karakoram International University, Gilgit-Baltistan. His current academic interests include portfolio optimisation, stochastic control problems, operational research and financial risk analysis.

Anoushe Sheharnaz Hussan (LUMS Faculty)

Anoushe graduated from LUMS in 2011 with a BSc. Honors in Mathematics and a minor in Economics. She holds two MSc degrees from the University of Western Ontario (Financial Mathematics and Pure Mathematics). Anoushe has over five years of industry experience; she was heading a team of quantitative analysts at the Bank of Montreal’s Model Validation group, responsible for validating and approving the bank’s credit risk models. She is currently a faculty member at the Mathematics Department at LUMS. mathematics/casm-workshop-mathematical-and-computational-finance